July 2013
Volume 13, Issue 9
Free
Vision Sciences Society Annual Meeting Abstract  |   July 2013
Mach Bands: Contrast normalization?
Author Affiliations
  • Frederick Kingdom
    McGill Vision Research, Dept. Ophthalmology, McGill University, Montreal, Canada
Journal of Vision July 2013, Vol.13, 1146. doi:10.1167/13.9.1146
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      Frederick Kingdom; Mach Bands: Contrast normalization?. Journal of Vision 2013;13(9):1146. doi: 10.1167/13.9.1146.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Aim. Mach bands are the illusory bright and dark bars seen at the knees and feet of luminance trapezoids. The most popular account of Mach bands is that they result from a feature coding process that generates a sparse, binary representation of luminance discontinuities in terms of ‘edges’ and ‘bars’. According to this account, the feet and knees of trapezoids elicit relatively strong responses in even-symmetric filters, and these are interpreted as indicative of bars. The filter responses to step-edges on the other hand are interpreted as indicative of edges not bars, predicting correctly no Mach bands at step-edges. Here I show through a modelling exercise that a simpler and more parsimonious explanation of Mach bands suffices that is in keeping with recent multi-scale filtering models of brightness coding: Mach bands result from contrast normalization. Method. One-dimensional representations of stimuli were convolved with a bank of one-dimensional, 2[sup]nd[/sup]-Derivative-of-Gaussian filters that formed a complete basis set. Each convolution response was multiplied by 1/(1+kAs), where As is the amplitude response of each scale (s) of filter, and k is a factor that determines the amount of contrast normalization, set to unity for all filters and all stimuli. Filter responses were then summed to produce a predicted brightness profile. Results. Mach bands were observed in trapezoids, and Generalized Gaussian edges with exponents >1. Mach bands were not observed in step-edges, Hilbert-transformed trapezoids, trapezoids in which all phases were set to 90deg, and Generalized Gaussian edges with exponents <=1. All results are in line with psychophysical observation. Conclusion. Mach bands are caused by contrast normalization, not feature coding.

Meeting abstract presented at VSS 2013

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